The 29-year-old's brace vindicated the choice of the Madrid boss Zinedine Zidane who decided to play the French striker despite poor returns of only one goal in his previous 12 games.
"He deserved to score. Karim has worked hard and he has never given anything less than his all," Zidane told BeINSport.
While Benzema's first was a text book far post header, his brace came moments into the second half due to a poacher's instinct.
Under pressure on Real's left flank, Corentin Tolisso passed the ball back to goalkeeper Sven Ulreich. But he failed to control it and slipped in front of an onrushing Benzema.
The gleeful forward rolled it into an empty net.
Though Joshua Kimmich and James Rodriguez got on the scoresheet for the Germans, the visitors could not find a tie-winning third goal.
Real hoping for Uefa Champions League record
Madrid stand one game away from becoming the first side to collect three Uefa Champions League crowns on the trot since 1997 when the competition emerged from the European Cup. That tournament had only been open to winners of the leading European leagues.
Before the revamp, seven clubs, inlcuding Madrid, had won three consecutive trophies. Bayern are among that elite and travelled to Madrid aiming to reach the final for the first time since their triumph over Borussia Dortmund in 2013.
Jupp Heynckes led the victory celebrations for the Bavarians on that night at Wembley.
Heynckes fails to win treble
He retired on the back of that high but was called away from his home in the hills to take the helm in October 2017 after Bayern's disastrous start to the Bundesliga and Champions League campaign under Carlo Ancelotti.
Having secured the 2018 Bundesliga title, 72-year-old Heynckes had been hoping to repeat his treble of 2013 in which Bayern also claimed the German Cup.
"My team played an outstanding game," he said. "I haven't seen Bayern play as well as that for years but at this high level you can't make the sort of mistakes we made after half-time."
Two years ago, Zidane entered the record books when he became the seventh man to win the European Cup/Champions League as a player and as a coach.
With Madrid's progress to the final in Kiev on 26 May against Liverpool or Roma, he can join Ancelotti and Bob Paisley as the only other managers to have won Europe's premier club competition three times.
"You always have to believe," said Madrid captain Sergio Ramos. "Real's DNA pushes you to fight until the end, we know how to stay together and suffer and that has taken us to the final. That is the soul of this team."